Employment minister Priti Patel, who is backing a vote to leave the EU, said Sir John was a "respected former prime minister" but it would be the public - not politicians - who would decide the outcome of the referendum.

The UK votes on whether to stay in or leave the European Union on 23 June.

David Cameron is campaigning for a Remain vote, as is most of his cabinet, but the party is deeply split over the issue, with many of its MPs supporting an exit.

In a hard-hitting speech in Oxford, Sir John - whose seven years in Number 10 were dominated by internal party rows over Europe - said the Remain side must "debunk myths" about immigration, sovereignty and the economy if it was to prevail.

He claimed that economic facts were simply "brushed aside" by Vote Leave and that those who favoured an EU exit were propagating "absurd falsehoods".

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"There is no shortage of their exaggerations," said Sir John, citing the cost of being in Europe as a "clear example".

"(UKIP leader) Nigel Farage, Iain Duncan Smith and Boris Johnson all put it at £20bn a year - it's even on Boris's battle bus; Michael Gove is more modest at £18bn (£350m a week), all of which, they tell us - if only we could be free of Europe - would be spent on the health service and our hospitals.

But he said their figures were "wrong" and said they should apologise for "peddling a clear cut untruth".

Sir John also dismissed arguments made by Leave campaigners, including Mr Johnson, that an EU exit would boost Britain's sovereignty.

"We should not forget that - in well over 90% of the votes cast in Brussels - the UK wins," he said.

"The caricature that we are repeatedly voted down in Europe is ill-informed nonsense."

'Pure demagoguery'

The former prime minister also took issue with some of the Leave campaign's rhetoric on immigration.

He claimed senior Tories were "morphing" into UKIP by pandering to immigration fears and warned it risked creating "long-term divisions" in society.

He singled out for criticism claims made by pro-exit campaigners - including Mr Gove - that EU expansion would open Britain's borders up to another 88 million people.

Image copyrightGetty ImagesImage caption
Sir John took issue with claims made by Boris Johnson (pictured) and other Vote Leave campaigns about the cost to the UK of EU membership

"I assume this distortion of reality was intended to lead the British people into believing that almost the entire population of possible new entrants will wish to relocate to the UK.

"If so, this is pure demagoguery. I hope that - when the heat of the referendum is behind us - the proponents of such mischief making will be embarrassed and ashamed at how they have misused this issue," he said.

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Sir John said he did not want to "silence" debate on immigration, as it was a "legitimate" issue - but he warned that "care honesty and balance" was needed to avoid "raising fears or fuelling prejudice".

Pro-exit justice minister Mr Raab said people cared about the "pressure" immigration puts on wages and public service, adding: "I think we're trying to handle a very serious issue responsibly."

He pointed to data published by the Office for National Statistics on Thursday showed a "massive under-estimate" in the amount of EU immigration into the UK, and said: "If Sir John Major or anyone else campaigning to stay in the EU wants to make the case that that's just the price we've got to pay then he can make that argument.

"But let's have the debate on the substance, not name-calling."

Image copyrightGetty ImagesImage caption
Pro-Brexit MP and minister Penny Mordaunt (l) said the public were concerned about the impact of immigration

Meanwhile, Conservative MP Peter Lilley, a former minister under Sir John, also said Vote Leave had got the tone right on immigration and suggested Sir John was "inventing a straw man".

"He was saying there is misuse of the issue - and that certainly would be wrong - but he didn't give any examples of this misuse," Mr Lilley added.

Conservative David Davis said it was "grossly unfair" to dismiss concerns about immigration as "UKIP".

"Sir John is right to warn that debates on immigration must not slip into xenophobia. But there are also great dangers from ignoring the very real concerns of the voters, and dismissing them as divisive and prejudiced," he said.